Turkey made a decision to launch the airstrikes just days after US President Donald Trump chose to withdraw US troops from northern Syria. A Syrian war monitoring group, the United Kingdom -based Syrian Observatory for Human Rights, reported Wednesday that people were fleeing the border town of Tal Abyad, which Turkey is expected to attack first.
This comes days after the United States troops backed away from the border area.
SDF fighters armed with rocket launchers were later seen deploying in the area of Ras al-Ain.
In the build-up to the offensive, Syria had said it was determined to confront any Turkish aggression.
Erdogan, announcing the start of the action, said the aim was to eliminate what he called a "terror corridor" on Turkey's southern border.
Trump later cast his decision to pull back US troops from parts of northeast Syria as fulfilling a campaign promise to withdraw from the "endless war" in the Middle East.
Turkey was taking over leadership of the fight against Islamic State in Syria, he said. Human rights groups have warned that any escalation of fighting in the area could displace hundreds of thousands more people. Trump had come under considerable condemnation for abandoning the Syrian Democratic Forces (SDF), its main ally in the battle against the Islamic State of Iraq and the Levant (ISIL or ISIS) armed group.
After appearing to give a green light to the Turkish invasion, he later threatened to "obliterate" Turkey's economy if it went too far.
In the U.S., Republican critics and others said he was sacrificing an ally, the Syrian Kurdish forces, and undermining Washington's credibility.
Turkey "has legitimate security concerns" after suffering "horrendous terrorist attacks" and hosting thousands of refugees, said NATO Secretary-General Jens Stoltenberg.
Turkey has been massing troops for days along its border with Syria and vowed it would go ahead with the military operation and not bow to the USA threat.
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European Union chief Jean-Claude Juncker on Wednesday demanded Turkey halt its military operation in northern Syria, telling Ankara the bloc would not pay for any so-called "safe zone" that might be created.
"I urge President Trump to change course while there is still time by going back to the safe zone concept that was working", said Graham, who also took his message to "Fox and Friends", a favorite show of the television-loving U.S. leader.
Fahrettin Altun, the Turkish presidency's communications director, called on the worldwide community to rally behind Ankara, which he said would also take over the fight against the Islamic State group.
Erdogan discussed the incursion by phone with Russian President Vladimir Putin.
Kurdish politician Nawaf Khalil, who is in northern Syria, said some people were leaving the town for villages farther south.
"At this stage we call on all the parties to exercise maximum restraint and to ensure the protection of civilians particularly", he told reporters Wednesday.
"We are concerned about what we're seeing of the actions of the Turkish Government moving into Syria, and what that could mean for the safety of people in that area", he said.
Chaos could present Islamic State with an opportunity to stage a revival and the SDF has been conducting operations against IS sleeper cells since capturing its final territorial foothold earlier this year. The Syrian Kurdish-led administration said it is responding positively to calls from Moscow encouraging the Kurds and the Syrian government to settle their difference through talks.
Turkey has carried out two previous incursions into northern Syria in recent years with the help of Syrian rebels. It was also ready to embrace "prodigal sons", it said, in an apparent reference to the Syrian Kurdish authorities who hold the northeast.
"Such reckless attitude to this highly sensitive subject can set fire to the entire region, and we have to avoid it at any cost", he said in Kazakhstan. Trump has denied he had abandoned the forces, the most capable USA partners in fighting ISIS in Syria.
In the IS attack, three suicide bombers struck Kurdish positions in Raqqa. There were no immediate reports of casualties there.
IS claimed an overnight suicide attack by two of its fighters in its former Syria stronghold of Raqa.